Fourier transform (FT) is a powerful tool to detect frequency of ion oscillations in ion traps, and based on this the FT mass spectrometry (FTMS) has been developed. Numerous studies have been carried out and methods have been implemented for the precise determination of oscillation frequencies and resolution improvement. For instance, calibration of frequency axis with special functions and usage of absorption mode (A-mode) of frequency spectrum have been tried.
However, to date not much attention has been paid to quantitative measurements for each peak in the spectrum. In other words, having generated a frequency (and consequently an m/z) spectrum one may want to know the actual number of ions that correspond to each peak of interest in the spectrum.
In conventional mass spectrometers, ions hit a detector thereby giving a measured signal where the number of ions can be evaluated by ion detector calibration. For example, a response function measured for certain parameters (ion energy, HV applied to parts of detector) is applied to the measured signal to get the real number of ions hit detector. Where the response function is constant the conversion of the measured signal to the real ion number is achieved simply by multiplication of a constant. There is no interference of ions of different m/z when such a detection technique is used. In other words, when two group of ions partially overlap each other when the detection occurs, the additivity is held and the peak integration of the resulting spectrum typically gives direct sum of the number of ions in each group.
However, in FTMS where detection is substantially different, artificial effects can take place. Briefly, the measurement routine includes injection of ions of different m/z values inside an ion trap where they can be trapped and perform oscillations during a relatively long time without changes (or with minor changes) of oscillation period. Oscillation period (or frequency) of ion(s) of each m/z value has its own value which can be measured by FT analysis.
As ions oscillate in the trap they pass one or more electrodes (typically referred to as pick-up electrodes) generating pulses of (image) charges on them which are measured in the time domain, and which can be referred to as a time domain signal. This time domain signal is measured over a certain acquisition time; the longer the acquisition time the better the frequency resolution of the frequency spectrum. The time domain signal is converted to a frequency domain signal in the frequency domain, for example using standard DFT (discrete Fourier Transform) algorithms. Thus, a frequency spectrum in complex values is obtained:f(t)→F(v)=Re(v)+iIm(v)f(t) represents a time domain signal, Re represents the real part of the FT, Im represents the imaginary part of the FT, v is the frequency. The frequency spectrum can be plotted as Re(v), Im(v) or M(v) whereM(v)=√{square root over (Re2+Im2)}where M(v) is the magnitude of the FT, and is related to F(v) via phase factor:F(v)=M(v)eiφ(v),where ϕ(v) is the phase.
In the simplest case, n ion clouds (each one having a certain m/z value, i.e. mass to charge ratio) would give n peaks on a M(v) plot for example.
In FTMS, the M(v) spectrum (magnitude mode, or M-mode, spectrum) is widely used for the mass spectrum representation. The advantages of M-mode are non-negative values of a spectrum, and it contains information from both real and imaginary part of frequency domain.
Peak intensity, which reflects respective ion species abundance in a spectrum, is typically evaluated on the basis of the amplitude of a peak of interest. This is the simplest and most straightforward way to make quantitative deductions from spectra. In other words, peak amplitude measurement is the simplest way of getting peak intensities indicative of ion abundances.
However, it is only possible to correctly quantify (quantize) the number of ions of a particular ion species in this way if peaks, e.g. adjacent peaks in the spectrum, do not perturb (interfere with) each other and if they all have an identical shape, e.g. a Gaussian or Lorentzian peak shape.
Integration of a peak in an M-mode spectrum, to obtain the area under the peak and thus a value for the peak intensity, can also be implemented as shown in “Kevin L Goodner et al. JASMS 1998, 9, 1204-1212” where detailed analysis has been performed on which window functions and fitting function are better for spectra represented in M-mode. Subsequently, peak intensity can be converted into an absolute value for the number of ions which were subject to analysis in the ion trap. This integration based method is supposed to give correct relative ion abundances especially for the case where the ions spatial spread dependent on its charge density during oscillations. However, it is proved that it doesn't work for M-mode spectra when there exist signal interferences.
In particular, it was found particularly problematic for FTMS to determine accurately the abundances of isotopes of the same ion using this technique. Typically, isotope ratios measured from mass spectra peak intensities obtained from image charge signal in an ion trap give values deviated from theoretical ones by significant amounts.
This is because of several reasons. For example, there is often interference between multiple close isotope peaks. Also, different ion clouds have respectively different decay rates with different abundances in the conditions when self-bunching may occur.
U.S. Pat. No. 5,436,447 describes a method of determining ion abundances in ICR FTMS using wavelet transforms. The wavelet transform intensity of a certain frequency peak is determined as a function of time and fitted with exponential decay in order to accurately find relative ion abundances at the starting time (end of excitation). Journal of the American Society for Mass Spectrometry, James A Bresson et al., 1998, 9, 799-804 discusses correction of isotopic abundance in FTICR mass spectra via time-domain data extraction. A peak of interest in frequency domain is isolated and reverse FT gives a time-domain signal for the individual mass-to-charge ratio. In the same manner, the relative ion abundances are given by the ratio of the obtained individual time domain signals.
However, the methods described in these prior art documents suffer from inaccuracies when adjacent peaks are located close enough to disturb true time-domain signal for an individual ion group obtained by inverse FT. Further, the accuracy of a recovered individual time-domain signal strongly depends on peak shape in the frequency domain. Extrapolation of individual time-domain signals via exponential decay can be used to account for damping of the signal as a cause of ion-gas collisions, but it does not account sufficiently for other kind of signal decays or modifications; for example self-bunching, which can prevail in UHV (ultra-high vacuum) conditions.
Also, the prior art methods described in these prior art documents suffer the drawback that additional time is required for performing FT and reverse FT operations.
An alternative prior art method is disclosed in the American Society for Mass Spectrometry 2014 Abstracts, Hans Pfaff, poster ThP540 (“FTMS-based isotopic simulator improves accuracy of mass and intensity measurements”). To identify measured isotopic pattern a search is performed using existing table patterns. A set of patterns is taken and is converted to frequency spectra and then into time-domain signal using inverse FT. These simulated time domain signals undergo a standard FFT procedure to get frequency spectra and correspondent mass spectra. The experimental isotopic pattern of interest is compared with the simulated patterns to find the best approximation which allows to attribute the pattern to a compound. The method allows to identify the compound despite the FT artefact effects which suppress amplitudes when there are several unresolved (or partially resolved) peaks. This method works under assumptions that peak shapes are identical, but this is not always true. Furthermore, this method cannot be applied for unknown isotopic pattern compounds which are not listed in databases, for example.
There are recent reports on using absorption mode (A-mode) spectra to represent the mass spectrum. The absorption mode spectrum (A-mode) is the part Re(v) of a spectrum of phase corrected F(v) dependence. A-mode was found to provide better resolution of spectra as it reveals about two times better resolution compared to M-mode without any additional information (raw data) recorded [Yulin Qi e al., JASMS 2011, 22:138-147]. Another publication (Yulin Qi et al., Anal. Chem. 2012, 84, 2923-2929) discusses the use of absorption mode Fourier transform mass spectra. Although absorption mode (A-mode) with various kind of window functions (apodization) is disclosed in these prior art documents, the aim of the research discussed in the documents is to improve the mass resolution and/or signal to noise ratio. However, the documents do not address the desire to quantify accurately the numbers of ions for any given peak, and do not consider how to achieve this in view of neighbouring peak interference and space charge interaction effects.
Accordingly, the prior art does not deliver a method of accurately determining the real ion abundances (relative values of quantitative values of ions) from the peak intensity, for example when the number of ions in the sample causes space charge interactions. In other words, the prior art does not deliver a method of accurately quantifying the number of ions in a particular ion species in an ion sample, for example when the number of ions in the sample causes space charge interactions.
In particular, the prior art methods do not provide techniques for determining the true ion abundances in a sample by measuring peak intensity of a mass spectrum (in the frequency domain) after Fourier transform of an acquired signal, which avoids the deviation from the real ion abundances associated with the respective peaks; e.g. where the peak(s) consist of multiple unresolved sub-peaks. As mentioned above, this is particularly problematic where the sub-peaks are a consequence of the presence of multiple isotopes of the same or similar ions in the measured sample.